**"Geometric series"**

## February 8 More Lesson Activities to Develop Understanding and Skills

*By toni On 5 February, 2021 · Leave a Comment*

REPETITION – writing rational numbers as fractions

DIFFERENCES OF SQUARES AND AREA

DIFFERENCES OF SQUARES INVESTIGATION

INTERSECTIONS Simultaneous Linear Equations

GP ALGEBRAICALLY Geometric series

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(1) […]

## Sierpinski Number and Shape Patterns

*By toni On 16 November, 2020 · 2 Comments*

There are many investigations and projects you could do based on the Sierpinski Tetrahedron.

For a start: how many small tetrahedra, like the blue model shown, were used to make the 6.5 metre high red balloon model shown below.

The smallest tetrahedron (Stage 0), the blue model, is made from 6 balloons, each […]

## Years 10 to 12 The von Koch Curve

*By toni On 10 September, 2019 · Leave a Comment*

Image starting with an equilateral triangle and replacing each edge by a zig-zag curve made up of 4 pieces. Each of the 4 pieces is one third of the length of the line segment it replaces so it looks as if equilateral triangles have been attached to the shape. Now imagine repeating […]

## NA5 GROWTH AND DECAY – FINANCIAL MATHEMATICS

*By toni On 28 August, 2018 · Leave a Comment*

This workshop guide provides learning activities that explore the ways in which arithmetic and geometric series are used in simple and compound interest calculations related to loans (including pay-day loans) , investments, annuities, hire-purchase, inflation etc. and there is an explanation of how APR is calculated. Ideas are given for practical ways […]

## GP Algebraically

*By toni On 26 May, 2017 · Leave a Comment*

Multiply out these expressions:

What do you notice?

Does this pattern continue?

Can you prove it?

What does this tell you about the sum to n terms of the geometric series with first term 1 and common ratio r?

Why do we get a formula for all values of r except r = 1?

Explain […]

## GP Geometrically

*By toni On 12 January, 2017 · Leave a Comment*

The squares in the diagram are to help us visualise an infinite geometric sum and we are not summing the areas of the squares, simply the lengths along the x-axis. The squares have side lengths given by powers of r: where 0 < r < 1 .

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